partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / fsle_fsle.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
index e9ebfb3811409c5865dd46c5f61bf3ec2bcb51d7..7dafa423bfc2e97ccc46766c90ca3cffc06d9458 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
@@ -25,8 +25,8 @@ lemma fsle_frees_trans:
       ∃∃n1,n2,f1. L1 ⊢ 𝐅+❪T1❫ ≘ f1 & L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #f1 #g2 #Hf1 #Hg2 #HL #Hn #f2 #Hf2
 lapply (frees_mono … Hg2 … Hf2) -Hg2 -Hf2 #Hgf2
-lapply (tls_eq_repl n2 … Hgf2) -Hgf2 #Hgf2
-lapply (sle_eq_repl_back2 … Hn … Hgf2) -g2
+lapply (pr_tls_eq_repl n2 … Hgf2) -Hgf2 #Hgf2
+lapply (pr_sle_eq_repl_back_dx … Hn … Hgf2) -g2
 /2 width=6 by ex3_3_intro/
 qed-.
 
@@ -47,7 +47,7 @@ lemma fsle_inv_frees_eq:
       f1 ⊆ f2.
 #L1 #L2 #H1L #T1 #T2 #H2L #f1 #Hf1 #f2 #Hf2
 elim (fsle_frees_trans_eq … H2L … Hf2) // -L2 -T2
-/3 width=6 by frees_mono, sle_eq_repl_back1/
+/3 width=6 by frees_mono, pr_sle_eq_repl_back_sn/
 qed-.
 
 lemma fsle_frees_conf:
@@ -56,8 +56,8 @@ lemma fsle_frees_conf:
       ∃∃n1,n2,f2. L2 ⊢ 𝐅+❪T2❫ ≘ f2 & L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
 #L1 #L2 #T1 #T2 * #n1 #n2 #g1 #g2 #Hg1 #Hg2 #HL #Hn #f1 #Hf1
 lapply (frees_mono … Hg1 … Hf1) -Hg1 -Hf1 #Hgf1
-lapply (tls_eq_repl n1 … Hgf1) -Hgf1 #Hgf1
-lapply (sle_eq_repl_back1 … Hn … Hgf1) -g1
+lapply (pr_tls_eq_repl n1 … Hgf1) -Hgf1 #Hgf1
+lapply (pr_sle_eq_repl_back_sn … Hn … Hgf1) -g1
 /2 width=6 by ex3_3_intro/
 qed-.
 
@@ -82,8 +82,8 @@ theorem fsle_trans_sn:
 * #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
 lapply (frees_mono … Hf0 … Hg0) -Hf0 -Hg0 #Hfg0
 elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct
-lapply (sle_eq_repl_back1 … Hf … Hfg0) -f0
-/4 width=10 by sle_tls, sle_trans, ex4_4_intro/
+lapply (pr_sle_eq_repl_back_sn … Hf … Hfg0) -f0
+/4 width=10 by pr_sle_tls, pr_sle_trans, ex4_4_intro/
 qed-.
 
 theorem fsle_trans_dx:
@@ -95,8 +95,8 @@ theorem fsle_trans_dx:
 * #n0 #n2 #f0 #f2 #Hf0 #Hf2 #Hn #Hf
 lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
 elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct
-lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
-/4 width=10 by sle_tls, sle_trans, ex4_4_intro/
+lapply (pr_sle_eq_repl_back_dx … Hg … Hgf0) -g0
+/4 width=10 by pr_sle_tls, pr_sle_trans, ex4_4_intro/
 qed-.
 
 theorem fsle_trans_rc:
@@ -109,8 +109,8 @@ theorem fsle_trans_rc:
 lapply (frees_mono … Hg0 … Hf0) -Hg0 -Hf0 #Hgf0
 elim (lveq_inj_length … Hm) // -Hm #H1 #H2 destruct
 elim (lveq_inj_length … Hn) // -Hn #H1 #H2 destruct
-lapply (sle_eq_repl_back2 … Hg … Hgf0) -g0
-/3 width=10 by lveq_length_eq, sle_trans, ex4_4_intro/
+lapply (pr_sle_eq_repl_back_dx … Hg … Hgf0) -g0
+/3 width=10 by lveq_length_eq, pr_sle_trans, ex4_4_intro/
 qed-.
 
 theorem fsle_bind_sn_ge:
@@ -120,9 +120,9 @@ theorem fsle_bind_sn_ge:
 #L1 #L2 #HL #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #p #I
 elim (fsle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
 elim (lveq_inj_void_sn_ge … H1n1 … H1n2) -H1n2 // #H1 #H2 #H3 destruct
-elim (sor_isfin_ex f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-<tls_xn in H2n2; #H2n2
-/4 width=12 by frees_bind_void, sor_inv_sle, sor_tls, ex4_4_intro/
+elim (pr_sor_isf_bi f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #f #Hf #_
+<pr_tls_swap in H2n2; #H2n2
+/4 width=12 by frees_bind_void, pr_sor_inv_sle_bi, pr_sor_tls, ex4_4_intro/
 qed.
 
 theorem fsle_flat_sn:
@@ -131,8 +131,8 @@ theorem fsle_flat_sn:
 #L1 #L2 #V1 #T1 #T * #n1 #x #f1 #g #Hf1 #Hg #H1n1 #H2n1 #H #I
 elim (fsle_frees_trans … H … Hg) -H #n2 #n #f2 #Hf2 #H1n2 #H2n2
 elim (lveq_inj … H1n1 … H1n2) -H1n2 #H1 #H2 destruct
-elim (sor_isfin_ex f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
-/4 width=12 by frees_flat, sor_inv_sle, sor_tls, ex4_4_intro/
+elim (pr_sor_isf_bi f1 f2) /2 width=3 by frees_fwd_isfin/ #f #Hf #_
+/4 width=12 by frees_flat, pr_sor_inv_sle_bi, pr_sor_tls, ex4_4_intro/
 qed.
 
 theorem fsle_bind_eq:
@@ -144,9 +144,9 @@ theorem fsle_bind_eq:
 * #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p #I1
 elim (lveq_inj_length … H1L) // #H1 #H2 destruct
 elim (lveq_inj_length … H2L) // -HL -H2L #H1 #H2 destruct
-elim (sor_isfin_ex f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-/4 width=15 by frees_bind_void, frees_bind, monotonic_sle_sor, sle_tl, ex4_4_intro/
+elim (pr_sor_isf_bi f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #f #Hf #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
+/4 width=15 by frees_bind_void, frees_bind, pr_sor_monotonic_sle, pr_sle_tl, ex4_4_intro/
 qed.
 
 theorem fsle_bind:
@@ -158,9 +158,9 @@ theorem fsle_bind:
 * #n2 #m2 #f2 #g2 #Hf2 #Hg2 #H2L #Hfg2 #p
 elim (lveq_inv_pair_pair … H2L) -H2L #H2L #H1 #H2 destruct
 elim (lveq_inj … H2L … H1L) -H1L #H1 #H2 destruct
-elim (sor_isfin_ex f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #f #Hf #_
-elim (sor_isfin_ex g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
-/4 width=15 by frees_bind, monotonic_sle_sor, sle_tl, ex4_4_intro/
+elim (pr_sor_isf_bi f1 (⫰f2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #f #Hf #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
+/4 width=15 by frees_bind, pr_sor_monotonic_sle, pr_sle_tl, ex4_4_intro/
 qed.
 
 theorem fsle_flat: